\newproblem{lay:4_4_3}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 4.4.3}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	Given the coordinate $[\mathbf{x}]_B=(1,0,-2)$ and the basis $B=\{(1,-2,3),(5,0,-2),(4,-3,0)\}$, find the vector $\mathbf{x}$.
}{
  % Solution
	The coordinates of $\mathbf{x}$ in the basis $B$ specify the linear combination of the vectors in the basis $B$ to find $\mathbf{x}$
	\begin{center}
		$\mathbf{x}=x_1\mathbf{b}_1+x_2\mathbf{b}_2+x_3\mathbf{b}_3=1\begin{pmatrix}1\\-2\\3\end{pmatrix}+0\begin{pmatrix}5\\0\\-2\end{pmatrix}
		   -2\begin{pmatrix}4\\-3\\0\end{pmatrix}=\begin{pmatrix}-7\\4\\0\end{pmatrix}$
	\end{center}
}
\useproblem{lay:4_4_3}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
